Policy invariance under affine transformations of the reward function?
This statement:


  (it is well-known that the optimal policy is invariant to positive affine transformation of the reward function).


is, as far as I know, and as you summarise, incorrect because simple translations to reward signal do affect the optimal policy, and the affine transform of a real number $x$ can be given by $f(x) = mx + c$

It is well known that optimal policy is unaffected by multiplying all rewards by a positive scaling, e.g. $f(x) = mx$ where $m$ is positive.

It is also worth noting that if an optimal policy is derived from Q values using $\pi(s) = \text{argmax}_a Q(s,a)$, then that policy function is invariant to positive affine transformations of action values given by $Q(s,a)$. Perhaps that was what the paper authors meant to write, given that they go on to apply normalisation to Q values.

The impact of the mistake is not relevant to the the rest of the paper as far as I can see (caveat: I have not read the whole paper).